| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , ⊢ |
| : , : , : |
1 | reference | 18 | ⊢ |
2 | instantiation | 4, 5 | ⊢ |
| : , : , : |
3 | instantiation | 6, 10, 7, 8* | , ⊢ |
| : , : |
4 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
5 | theorem | | ⊢ |
| proveit.physics.quantum.algebra.ket_zero_and_one_have_zero_inner_prod |
6 | axiom | | ⊢ |
| proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
7 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.zero_is_complex |
8 | instantiation | 9, 10 | , ⊢ |
| : |
9 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
10 | instantiation | 44, 11, 12 | , ⊢ |
| : , : |
11 | instantiation | 73, 53, 13 | ⊢ |
| : , : , : |
12 | instantiation | 21, 14, 15 | , ⊢ |
| : , : , : |
13 | instantiation | 73, 47, 16 | ⊢ |
| : , : , : |
14 | instantiation | 37, 24, 17 | , ⊢ |
| : , : |
15 | instantiation | 18, 19, 20 | , ⊢ |
| : , : , : |
16 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.e_is_real_pos |
17 | instantiation | 21, 22, 23 | , ⊢ |
| : , : , : |
18 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
19 | instantiation | 30, 72, 25, 31, 27, 32, 24, 38, 39, 34 | , ⊢ |
| : , : , : , : , : , : |
20 | instantiation | 30, 31, 58, 25, 32, 26, 27, 45, 28, 38, 39, 34 | , ⊢ |
| : , : , : , : , : , : |
21 | theorem | | ⊢ |
| proveit.logic.equality.sub_right_side_into |
22 | instantiation | 37, 29, 34 | , ⊢ |
| : , : |
23 | instantiation | 30, 31, 58, 72, 32, 33, 38, 39, 34 | , ⊢ |
| : , : , : , : , : , : |
24 | instantiation | 73, 53, 35 | ⊢ |
| : , : , : |
25 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat3 |
26 | instantiation | 40 | ⊢ |
| : , : |
27 | instantiation | 36 | ⊢ |
| : , : , : |
28 | instantiation | 73, 53, 43 | ⊢ |
| : , : , : |
29 | instantiation | 37, 38, 39 | , ⊢ |
| : , : |
30 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
31 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
32 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
33 | instantiation | 40 | ⊢ |
| : , : |
34 | instantiation | 73, 53, 41 | ⊢ |
| : , : , : |
35 | instantiation | 42, 49, 43 | ⊢ |
| : , : |
36 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
37 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_complex_closure_bin |
38 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.i_is_complex |
39 | instantiation | 44, 45, 46 | , ⊢ |
| : , : |
40 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
41 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._phase_is_real |
42 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
43 | instantiation | 73, 47, 48 | ⊢ |
| : , : , : |
44 | theorem | | ⊢ |
| proveit.numbers.exponentiation.exp_complex_closure |
45 | instantiation | 73, 53, 49 | ⊢ |
| : , : , : |
46 | instantiation | 50, 51 | , ⊢ |
| : |
47 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
48 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
49 | instantiation | 73, 56, 52 | ⊢ |
| : , : , : |
50 | theorem | | ⊢ |
| proveit.numbers.negation.complex_closure |
51 | instantiation | 73, 53, 54 | , ⊢ |
| : , : , : |
52 | instantiation | 73, 59, 55 | ⊢ |
| : , : , : |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
54 | instantiation | 73, 56, 57 | , ⊢ |
| : , : , : |
55 | instantiation | 73, 71, 58 | ⊢ |
| : , : , : |
56 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
57 | instantiation | 73, 59, 60 | , ⊢ |
| : , : , : |
58 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
59 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
60 | instantiation | 73, 61, 62 | , ⊢ |
| : , : , : |
61 | instantiation | 63, 64, 65 | ⊢ |
| : , : |
62 | assumption | | ⊢ |
63 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.int_interval_within_int |
64 | instantiation | 66, 67, 68 | ⊢ |
| : , : |
65 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.zero_is_int |
66 | theorem | | ⊢ |
| proveit.numbers.addition.add_int_closure_bin |
67 | instantiation | 69, 70 | ⊢ |
| : |
68 | instantiation | 73, 71, 72 | ⊢ |
| : , : , : |
69 | theorem | | ⊢ |
| proveit.numbers.negation.int_closure |
70 | instantiation | 73, 74, 75 | ⊢ |
| : , : , : |
71 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
72 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
73 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
74 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_int |
75 | assumption | | ⊢ |
*equality replacement requirements |